Measuring hidden phenotype: Quantifying the shape of barley seeds using the Euler Characteristic Transform

Shape plays a fundamental role in biology. Traditional phenotypic analysis methods measure some features but fail to measure the information embedded in shape comprehensively. To extract, compare, and analyze this information embedded in a robust and concise way, we turn to Topological Data Analysis (TDA), specifically the Euler Characteristic Transform (ECT). TDA measures shape comprehensively using mathematical terms based on algebraic topology features. To study its use, we compute both traditional and topological shape descriptors to quantify the morphology of 3121 barley seeds scanned with X-ray Computed Tomography (CT) technology at 127 micron resolution. The ECT measures shape by analyzing topological features of an object at thresholds across a number of directional axes. We optimize the number of directions and thresholds for classification to 158 and 8 respectively, creating vectors of length 1264 that are topological signatures for each barley seed. Using these vectors, we successfully train a support vector machine to classify 28 different accessions of barley based on the 3D shape of their grains. We observe that combining both traditional and topological descriptors classifies barley seeds to their correct accession better than using just traditional descriptors alone. This improvement suggests that TDA is thus a powerful complement to traditional morphometrics to describe comprehensively a multitude of shape nuances which are otherwise not picked up. Using TDA we can quantify aspects of phenotype that have remained "hidden" without its use, and the ECT opens the possibility of accurately reconstructing objects from their topological signatures.